Question

The weights of steers in a herd are distributed normally. The standard deviation is 100lbs and the mean steer weight is 1300lbs. Find the probability that the weight of a randomly selected steer is between 1169 and 1400lbs. Round your answer to four decimal places.

Answer 1

So in order to find the probability that the weight of a randomly selected steer is between 1169lbs and 1400lbs we first need to find the z values corresponding to 1169 and 1400. The z values are calculated by using the mean and the standard deviation of the population of steers:

`z(x)=(x-\mu)/(\sigma)`

Where mu is the mean and sigma the standard deviation. Then we have:

`z(x)=(x-1300)/(100)`

And the two z values that we need are:

`\begin{gathered} z(1169)=(1169-1300)/(100)=-1.31 \\ z(1400)=(1400-1300)/(100)=1 \end{gathered}`

Then we look at a z value table and see the values corresponding to these two z values:

So the values given by the table are 0.0951 and 0.8413. This means that the probability that the weight of a randomly selected steer is between 1169lbs and 1400lbs is 0.8413-0.0951=0.7462. Then the answer is 0.7462.